lwilliams1922, you're not doing anything wrong. I don't know anyone who braids firmly with extensions the first time they do it. That will come with practice.
I never wrap the additional hair around the base. I just have it divided into two sections one being thinner than the other, then I cross the thinner hair in the middle over the thicker strand as if making a + sign and fold the hair over so that the ends of the thin sections meet. (See #1-4 below ) So now I have 3 sections. I usually place that cross over section at the base of the hair I want to braid; ie behind my hair and using my thumb I hold the cross over point against the base of my hair and my index finger or middle finger holds the front of my hair, so between thumb and middle finger I firmly hold the hair in place. (#6) I then use the fingers of the other hand to pull out 1/3 of my hair to match it with one arm of the extension hair. I then use the thumb and fingers of the hand that was free to hold hair in place while the other hand is free to pull out the arm on the other side of my hair that will match the arm of the extension hair, leaving the central arm.
Then I start braiding #7, making sure that there's a thumb and finger of one hand is holding the hair while index finger reach over to grab extension hair and my hair together to bring them over central section. (I braid over, not under.); then transfer the base hold to other hand's fingers. There's no pulling; just making sure that my fingers and thumb are holding the extension hair against my own hair.
The photos below were my attempt at showing what I just described but I obviously failed miserably.
#9 was taken to show you that you should not be holding your hair so high up from the cross over point while braiding . You need to do it like #10 shows. Fingers should be close to the cross-over so you can do a good braid. #8 just shows that your own hair should be divided into 3 parts like the extension hair.
But don't expect to be good on your first or second or third try.
The way I got it was first I got my first install done by my stylist, then I'd undo one in the back and try to redo it. Then I'd try with another. I also had my baby sister to practice on. After a few lousy attempts, I was able to redo all my braids working on one at a time. After that, I never looked back. So just know practice will make perfect.